Faltings's product theorem

In arithmetic geometry, the Faltings's product theorem gives sufficient conditions for a subvariety of a product of projective spaces to be a product of varieties in the projective spaces. It was introduced by Faltings (1991) in his proof of Lang's conjecture that subvarieties of an abelian variety containing no translates of non-trivial abelian subvarieties have only finitely many rational points. (Evertse 1995) and (Ferretti 1996) gave explicit versions of the Faltings's product theorem.

References

• Evertse, Jan-Hendrik (1995), "An explicit version of Faltings' product theorem and an improvement of Roth's lemma", Acta Arithmetica 73 (3): 215–248, doi:10.4064/aa-73-3-215-248, ISSN 0065-1036, http://matwbn.icm.edu.pl/ksiazki/aa/aa73/aa7332.pdf 
• Faltings, Gerd (1991), "Diophantine approximation on abelian varieties", Annals of Mathematics, Second Series 133 (3): 549–576, doi:10.2307/2944319, ISSN 0003-486X 
• Ferretti, Roberto (1996), "An effective version of Faltings' product theorem", Forum Mathematicum 8 (4): 401–427, doi:10.1515/form.1996.8.401, ISSN 0933-7741